Baseline Cactus Size
Malory Owen, York University, Lortie Lab
1/20/2019
Let’s explore the size, abundance, health, and locals of three different potential study species.
- Buckhorn Cholla: Cylindropuntia anthrocarpa
- Silver Cholla: Cylindropuntia enchinocarpa
- Beavertail: Opuntia basilaris
Buckhorn Cholla, Cylindropuntia anthrocarpa
Silver Cholla, Cylindropuntia echinocarpa
Beavertail, Opuntia basilaris
How do they measure up? Before any size-binning can be done for the bird double-mutualism experiment, we need to measure a sample of a population of cacti we’ll be working from. We’ll also need to know which species we even want to work with! Some barriers our study species need to overcome are size, size variability, abundance, and health. After all, we want a tall-ish species (so pollinators and frugivors are interested enough), with plenty of variability in size to test that, and enough of them to manipulate conditions, and healthy enough so we can expect some flowers and fruit later on. And for fun, let’s take a quick look at shrubs to see if they’re associated with cacti in any respect.
Data: What are the cacti?
head(cholla) #see a bit of the data## # A tibble: 6 x 23
## transect transect_start_~ transect_start_~ transect_end_lat
## <int> <dbl> <dbl> <chr>
## 1 1 34.8 116. 34.78203
## 2 1 34.8 116. 34.78203
## 3 1 34.8 116. 34.78203
## 4 1 34.8 116. 34.78203
## 5 1 34.8 116. 34.78203
## 6 1 34.8 116. 34.78203
## # ... with 19 more variables: transect_end_lon <chr>, meter <int>,
## # cactus_id <chr>, cactus_number <chr>, species <chr>,
## # distance_meters <dbl>, x <dbl>, y <dbl>, z <dbl>, primary <int>,
## # secondary <int>, tertiary <int>, quaternary <int>, health_index <int>,
## # cactus_lat <dbl>, cactus_lon <dbl>, shrub_present <chr>,
## # shrub_alive <chr>, species_letter <chr>head(opuntia) #and for opuntia## # A tibble: 6 x 14
## cactus_id species x y z primary secondary tertiary quaternary
## <int> <chr> <dbl> <dbl> <dbl> <int> <int> <int> <int>
## 1 1 Opunti~ 0.15 0.15 0.15 13 1 0 0
## 2 2 Opunti~ 0.3 0.4 0.2 24 3 0 0
## 3 3 Opunti~ 0.2 0.3 0.2 11 4 0 0
## 4 4 Opunti~ 0.2 0.2 0.1 5 3 0 0
## 5 5 Opunti~ 0.1 0.15 0.1 6 0 0 0
## 6 6 Opunti~ 0.4 0.4 0.15 11 35 6 0
## # ... with 5 more variables: health_index <int>, cactus_lat <dbl>,
## # cactus_lon <dbl>, shrub_present <chr>, shrub_alive <chr>Location: Where are the cacti?
Let’s map and take a look at the cacti individuals sampled. For C. anthrocarpa, we were easily able to sample at every 5 meters along 5 transects that were spaced 5 meters a part (n=105). C. enchinocarpa, however, was a bit less dense, so after doing our first two transects 5 meters apart, we realized we needed to increase the distance between transects to 10 meters. We also weren’t able to get a cactus sampled at every 5 meters, and sampled 9 transects (n=98). The least common, however, was Opuntia basilaris, so rare that transects were ineffective and we instead unsystematically searched the entire site only to find a paltry number of individuals (n=26).
map <- leaflet() %>%
addTiles() %>%
addCircleMarkers(lng = -115.663, lat = 34.783, radius = 5, color = "#F4D99C", popup = "Sunset Cove") %>% #map center point for Sunset Cove
addCircleMarkers(lng = buckhorn$cactus_lon, lat = buckhorn$cactus_lat, radius = 5, color = "#D5DEAF", popup = "Buckhorn Cholla") %>% #Map buckhorn
addCircleMarkers(lng = silver$cactus_lon, lat = silver$cactus_lat, radius = 5, color = "#AFCEDE", popup = "Silver Cholla") %>% #map silver
addCircleMarkers(lng=opuntia$cactus_lon, lat = opuntia$cactus_lat, radius = 5, color = "#DEAFD6") #add opuntia
map #printClick on a point to see the species! (Green is Buckhorn Cholla, blue is Silver Cholla, and pink is Beavertail.)
We were able to sample 98 Silver Cholla (C. enchinocharpa) and 105 Buckhorn Cholla (C. anthrocarpa), but had to do nearly twice as many transects for the former (9 versus 5 transects). You can see the differences in densities for the two cholla species in the map above. However, we had to abandon the transect method and search haphazardly to find any Beavertail (Opuntia basilaris) at all. C. anthrocarpa is the densest cactus species at Sunset Cove, followed by C. enchinocarpa and then O. basilaris. Based on my proposed protocol, each study species needs 150 individuals to replicate each combination of variables 10 times. Ideally, the individuals manipulated between flowering and fruiting season will not be resampled in the the fruiting season, as our manipulation of the flowers in April may impact the number of fruit in August. This means that C. anthrocarpa is a solid study species option, C. enchinocarpa is certainly possible, but not as dominant as its cousin, and O. basilaris is out of the question.
Size of the cacti
We’ve seen the distribution of cacti, but size of the cacti is what’s really important for this study. We need to know if the sizes are variable enough to split into 3 class sizes (small, medium, and large), and have a general idea of their overal height, to consider if pollinating and frugivorous birds will engage with the flower and fruits of the cacti at all.
tapply(all$z, all$species, mean) #means height of each species## Cylindropuntia anthrocarpa Cylindropuntia echinocarpa
## 1.0380952 0.5529592
## Opuntia basilaris
## 0.1673077ggplot(all, aes(x = species, y=z)) +
geom_boxplot() + labs(title = "Size of Cacti", x = "Species", y = "Height in meters") +
theme_minimal() #no outliers
#Test for statistical difference between species
shapiro.test(buckhorn$z) #nearly normal##
## Shapiro-Wilk normality test
##
## data: buckhorn$z
## W = 0.97717, p-value = 0.06667shapiro.test(silver$z) #not normal##
## Shapiro-Wilk normality test
##
## data: silver$z
## W = 0.98532, p-value = 0.349shapiro.test(opuntia$z) #normal##
## Shapiro-Wilk normality test
##
## data: opuntia$z
## W = 0.88797, p-value = 0.008519#Because not everything is normal, let's do a non parametric version of ANOVA: Kruskall Wallis to test height of cacti
kruskal.test(species ~ z, data = all)##
## Kruskal-Wallis rank sum test
##
## data: species by z
## Kruskal-Wallis chi-squared = 151.52, df = 52, p-value = 1.158e-11#p < 0.0001, each cactus species has non-indentical heights. Variability for binning
One important variable of my project is size classes within a species: small, medium, and large. Because height is what may influence pollination and frugivory, I will use the “z-axis” that I measured as the factor for size.
Each size class must have enough individuals within it to replicate. I need to decide how to bin the size classes; either I must use natural breaks present in the data, or I must create equally-sized bins for the study species. Let’s examine each species size distribution, and make decisions about size class breaks upon that.
#Buckhorn Cholla size distribution
ggplot(buckhorn, aes(x = z)) +
geom_density() + labs(title = "Size of Cacti", x = "Buckhorn", y = "Height in meters") +
theme_minimal() #bimodal, ever so slightly
ggplot(silver, aes(x = z)) +
geom_density() + labs(title = "Size of Cacti", x = "Silver", y = "Height in meters") +
theme_minimal() #unimodal
ggplot(opuntia, aes(x = z)) +
geom_density() + labs(title = "Size of Cacti", x = "Opuntia", y = "Height in meters") +
theme_minimal()
None of the species have distributions with natural breaks (see density plots), and, especially for our two Cylindropuntia species, we can see that there are even distances between quartiles (see boxplots). For these reasons, I propose an equal-size binning method to determine size class.
But what exactly are the size classes then, for each species?
#Determine equal-sized size classes for cacti based on height (z)
minmax <- data.frame(
aggregate(z~species, data=all, min),
aggregate(z~species, data=all, max)) #create dataframe with min and max
bins <- mutate(minmax, range = z.1-z)
bins <- mutate(bins, bins = range/3) #divide by 3 (because 3 size classes wanted, small medium and large) to get differences between size classes
size_class_options <- mutate(bins, small = z) %>%
mutate(bins, medium = z + bins) %>%
mutate(bins, large = z.1 - bins) #create our size classes, each column represents the minimum value to start each size class.
#Make it pretty
#create vectors
species <- c("Cylindropuntia anthrocarpa", "Cylindropuntia enchinocarpa", "Opuntia basilaris")
small <- c("<85cm", "<45cm", "<15cm")
medium <- c("86cm - 152cm", "46cm - 72cm", "16cm - 22cm")
large <- c(">153cm", ">73cm", ">23cm")
#create dataframe for easy viewing
size_class <- data.frame(species, small, medium, large)
size_class## species small medium large
## 1 Cylindropuntia anthrocarpa <85cm 86cm - 152cm >153cm
## 2 Cylindropuntia enchinocarpa <45cm 46cm - 72cm >73cm
## 3 Opuntia basilaris <15cm 16cm - 22cm >23cm#Let's quickly visualize the size bins
ggplot(size_class_options, aes(x = species, y=bins)) +
geom_bar(stat = "identity") + labs(title = "Size of Bins", x = "Species", y = "Bins size (meters)") +
theme_minimal()
We’ve determined what our size classes would be for each species, and can see that Buckhorn Cholla (*C. anthrocarpa) has the largest class sizes, followed by Silver Cholla, and then Beavertail. Having large size classes may translate more clearly to birds, and therefore, be a suitable metric to measure if bird visitation is influenced by cactus size.
Health of the cacti
Another important factor to consider when exploring potential study species is their overall health. After all, are these individuals even capable of flowering and fruiting? To measure health, we created a health index based on the Wind Wolves Bakersfield Cactus Report, which classifies each individual’s health on a discrete scale of 1-5 (1 being the least healthy, and 5 being the healthiest). We considered overall paddle/branch death, as well as scarification and rot when determining health.
#What is the distribution of health index scores?
ggplot(all, aes(x = health_index)) +
geom_histogram() + labs(title = "Health of Cacti", x = "Number of individuals in each health class by species", y = "Health class") +
facet_grid(~species) +
theme_minimal()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
We can see that the Cylindropuntia species are the healthier than the Opuntia counterparts. The question is, will an unhealthy population still flower/fruit as much as a healthy population? Perhaps, but this is not the question of my project.
Conclusions: Who is America’s Next Top Cactus?
The Study Site, Sunset Cove